Concept:
Degree of saturation (S):
It is the ratio of volume of water to the volume of voids present in soil sample. Its value vary from 0 to 1.
\({\rm{S = }}\frac{{{{\rm{V}}_{\rm{w}}}}}{{{{\rm{V}}_{\rm{V}}}}}\)
Void ratio (e):
It is the ratio of volume of voids to the volume of solids present in soil sample. Void ratio of fine grained soid is greater than coarse grained soil.
\({\rm{e = }}\frac{{{{\rm{V}}_{\rm{V}}}}}{{{{\rm{V}}_{\rm{S}}}}}\)
Water content (w):
It is the ratio of weight of water to the weight of solids present in soil sample. Water content of fine grained soid is greater than coarse grained soil.
\({\rm{w = }}\frac{{{{\rm{W}}_{\rm{w}}}}}{{{{\rm{W}}_{\rm{s}}}}}\)
Specific gravity (G):
It is the ratio of unit weight of any substance to the unit weight of water.
\({\rm{G = }}\frac{{{{\rm{\gamma }}_{\rm{s}}}}}{{{{\rm{\gamma }}_{\rm{w}}}}}\)
The relationship between e and n is given by,
\({\rm{\;n}} = {\rm{}}\frac{{\rm{e}}}{{1\: + \:{\rm{e}}}}\)
The relationship between S, e, w and G is given by,
∴ Se = wG
Calculation:
Given,
Gs = 2.71, n = 40% = 0.4 and w = 20% = 0.2
The relationship between e and n is given by
\({\rm{n}} = {\rm{}}\frac{{\rm{e}}}{{1\: + \:{\rm{e}}}}\)
It can be written as,
\(\begin{array}{l} {\rm{e}} = \frac{{\rm{n }}}{{1 - {\rm{n }}}} \end{array}\)
\(\begin{array}{l} {\rm{e}} = \frac{{\rm{0.4 }}}{{1 - {\rm{0.4 }}}} \end{array}\)
e = 0.67
The relationship between S, e, w and G is given by
Se = wG
S × 0.67 = 0.2 × 2.71
S = 0.808 = 80.8% ≈ 81%
Hence the degree of saturation of the soil is 81%